Energy-momentum tensor in the 2d $O(3)$ non-linear sigma model on the lattice

TL;DR

This paper investigates the non-perturbative renormalization of the energy-momentum tensor in the 2d O(3) non-linear sigma model on the lattice, identifying operator mixing and outlining simulation strategies.

Contribution

It identifies all operators mixing with the energy-momentum tensor on the lattice and discusses methods for non-perturbative renormalization in the model.

Findings

Operators mixing with the energy-momentum tensor are identified.

Non-linear Ward identities constrain operator mixing.

Simulation techniques to reduce lattice artifacts are outlined.

Abstract

The long-term goal of this project is the non-perturbative renormalization of the energy-momentum tensor in the 2d $O(3)$ non-linear sigma model using different methods which have been developed for QCD applications. As a first step, we have identified all operators that mix with the energy-momentum tensor once a lattice discretization is employed, that is all which are compatible with power counting and with the symmetries of the theory. Since these operators are constrained by non-linear Ward identities arising from the non-linear realization of the $O(3)$ symmetry, this is not entirely straightforward on the technical level. We have also outlined the basics of ongoing numerical simulations with shifted boundary conditions and an optimized constraint action to minimize lattice artifacts.